Archimedes (287 B.c.e.–212 B.c.e.)

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Archimedes Summary

Archimedes (287 B.c.e.–212 B.c.e.)

Archimedes was a native of Syracuse, Sicily, the son of the astronomer Pheidias. The many achievements accredited to him include: showing that the value of π lies between the values 3 10/71 and 3 1/7 (this he obtained by circumscribing and inscribing a circle with regular polygons having 96 sides); showing that the problem of squaring the circle and rectifying its circumference were equivalent; developing a number system based on powers of myriad (10,000) to deal with large numbers; and establishing methods for finding the area under a parabola, a result that needed the integral calculus of Gottfried von Leibnitz and Isaac Newton by 2,000 years. His name is also attached to many fundamental ideas in hydrostatics and the use of levers.

Little is known of his early life other than that he studied in Alexandria and became friends with Conon, with whom he corresponded for many years. This correspondence is the source of much that is known of Archimedes mathematics. A good deal of his work survived only in Arabic translations of the Greek originals, and was not translated into Latin until 1543. Perhaps due to the high regard contemporaries had for his geometrical work, much of it survived. It was standard reading for scholars into the late seventeenth century, and would have been read by Leibnitz and Newton.

It is thought that Archimedes had a lower regard for his mechanical work; however, this is difficult to validate because few writings about his mechanical devices remain. Archimedes used mechanics as a tool to think about abstract problems, rather than as a field of study itself. Contemporaries such as Plato frowned upon such a link between geometry and mechanics; they considered it as a corruption of the purity of geometry.

Despite his preference for pure geometry, Archimedes was not adverse to dramatic demonstrations of his discoveries of force-enhancing devices such as levers. Reports tell that he was able to manipulate a fully laden ship single-handed, using a series of levers and pulleys, after which he is said to have exclaimed, "Give me a place to stand on and I will move the earth." Applications of these ideas were exploited by Hieron II in the Punic wars when Marcellus, a Roman General, attacked Syracuse in 214 B.C.E. Marcellus's pride and joy was a primitive siege engine mounted on eight galleys lashed together, but Archimedes built a variety of far more advanced machines to defeat him. These included catapults that could launch massive stones to crash down on the fleet and sink Marcellus's galleys, and other devices, using systems of levers and counterweights, capable of lifting an entire galley until it was upright on its stern, and then plunging it to the bottom.

Archimedes' mechanical skill, together with his theoretical knowledge, enabled him to construct many ingenious machines. During his time in Egypt, he invented a hand-cranked manual pump, known as Archimedes' screw, that is still used in many parts of the world. Its open structure is capable of lifting fluids even if they contain large amounts of debris.

Archimedes' fascination with geometry was beautifully described by Plutarch:

Oftimes Archimedes' servants got him against his will to the baths, to wash and anoint him; and yetbeing there, he would ever be drawing out of the geometrical figures, even in the very embers of the chimney. And while they were anointing of him with oils and sweet savours, with his fingers he drew lines upon his naked body; so far was he taken from himself, and brought into ecstasy or trance, with the delight he had in the study of geometry. Archimedes discovered fundamental theorems concerning the center of gravity of plane figures and solids. His most famous theorem, called Archimedes' Principle, gives the weight of a body immersed in a liquid.

The reference to Archimedes' Principle is in connection with another problem posed by Hieron II. The story tells of how Hieron, suspecting that a disreputable jeweler had adulterated a gold crown with silver, asked Archimedes to determine whether the crown was pure gold or not. Legend has it that Archimedes discovered a solution while in his bath, yelled "Eureka-I've found it" and ran off to the palace, neglecting to dress first! It is not know whether the goldsmith was guilty, but for the sake of the story it is usually assumed that he was.

The result that Archimedes discovered was the first law of hydrostatics, better known as Archimedes' Principle. Archimedes studied fluids at rest, hydrostatics, and it was nearly 2,000 years before Daniel Bernoulli took the next step when he combined Archimedes' idea of pressure with Newton's laws of motion to develop the subject of fluid dynamics.

As enigmatics Archimedes was in life, he is perhaps better remembered for his death. An account is given by Livy (59 B.C.E.–17 C.E.) History of Rome from its Foundation, Book XXV. It tells how Archimedes, while intent on figures that he had traced in the dust, and regardless of the hideous uproar of an army let loose to ravage and despoil a captured city, was killed by a soldier who did not know who he was. Another version, by Plutarch, recounts that Archimedes was intent on working out some problem by a diagram, and having fixed both his mind and eyes upon the subject of his speculation, noticed neither the entry of the Romans nor that the city was taken. A soldier unexpectedly came up to him and commanded that Archimedes accompany him. When he declined to do this before he had finished his problem, the enraged soldier drew his sword and ran him through. Yet a third account by John Tzetzes in the twelfth century Book of Histories (Chiliades), Book II, tells a similar story with a slight twist. It says that when Archimedes refused to stand clear of one of his diagrams when disturbed by a Roman soldier Archimedes cries out "Somebody give me one of my engines." The Roman, knowing that Archimedes' engines had defeated Marcellus's fleet, became frightened and slew him.